Problem Statement

You are in charge of controlling a dam. The dam can store at most $L$ liters of water. Initially, the dam is empty. Some amount of water flows into the dam every morning, and any amount of water may be discharged every night, but this amount needs to be set so that no water overflows the dam the next morning.

It is known that $v_i$ liters of water at $t_i$ degrees Celsius will flow into the dam on the morning of the $i$-th day. You are wondering about the maximum possible temperature of water in the dam at noon of each day, under the condition that there needs to be exactly $L$ liters of water in the dam at that time. For each $i$, find the maximum possible temperature of water in the dam at noon of the $i$-th day. Here, consider each maximization separately, that is, the amount of water discharged for the maximization of the temperature on the $i$-th day, may be different from the amount of water discharged for the maximization of the temperature on the $j$-th day $(j≠i)$.

Also, assume that the temperature of water is not affected by anything but new water that flows into the dam. That is, when $V_1$ liters of water at $T_1$ degrees Celsius and $V_2$ liters of water at $T_2$ degrees Celsius are mixed together, they will become $V_1+V_2$ liters of water at $\frac{T_1*V_1+T_2*V_2}{V_1+V_2}$ degrees Celsius, and the volume and temperature of water are not affected by any other factors.

Constraints

• $1≤ N ≤ 5*10^5$
• $1≤ L ≤ 10^9$
• $0≤ t_i ≤ 10^9(1≤i≤N)$
• $1≤ v_i ≤ L(1≤i≤N)$
• $v_1 = L$
• $L$, each $t_i$ and $v_i$ are integers.

Input

Input is given from Standard Input in the following format:

N L
t_1 v_1
t_2 v_2
:
t_N v_N

Output

Print $N$ lines. The $i$-th line should contain the maximum temperature such that it is possible to store $L$ liters of water at that temperature in the dam at noon of the $i$-th day.

Each of these values is accepted if the absolute or relative error is at most $10^{-6}$.